Smoothness and tangent bundles of arithmetical schemes

摘要

We study a notion of quasi-smoothness which makes possible to associate a canonical tangent bundle to certain arithmetical schemes (see [V1]). In this context we prove that we can associate a jacobian ideal to any irreducible subscheme. A class of regular centers, so that quasi-smoothness is preserved by blowing-up, will be enlarged and characterized by means of their jacobian ideal and some geometrical conditions, improving the results appearing in [V1].